MathDB

Let G (n) = max | A(n) |, where A(n) ranges over all subsets of {1,2,...,n} and contains no three-member geometric series, ie, there is no

x, y, z \in A

such that x < y < z and xz = y^2. Prove that

\lim_{n \to \infty} \frac{G (n)}{n}

exists.

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